[tetMitshisk]

There are two issues here:

1. Leaving the elbows/arms uncovered
2. Wearing clothing that one would not go out with in public.

As for the first, I have yet to come across a statement in any of the Hanafi books of fiqh, stating this to be Makruh. I have searched in detail, have asked numerous Muftis, but no one has been able to produce one such ruling from the reliable books of the madhab.

The Fiqh books mention the issue of folding sleeves, however this is makruh due to it being forbidden in Hadith, as one would be preventing the sleeves from making sajdah.

Some Urdu Fatawa use the texts on folding the sleeves for t-shirts, however those texts don't apply here.

As for the second, maybe 50 years ago, wearing a short-sleeve shirt or a T-shirt would have been something one would not wear out in public.
Today, people wear it everywhere, so it isn't classfied as thiyab al-bidhlah ie. clothing one wouldn't wear in public. It is makruh to perform salah in things like pyjama's, as these wouldn't be worn in public. Short-sleeves are not so.

So one is allowed to perform salah in clothing that is short-sleeved, as long as it is such clothing that one would normally wear in public.

As for Nabi's qamis sleeves being until the wrists, that doesn't necessitate shorter sleeves being makruh, just as it doesn't negate other items of Nabi having shorter sleeves. In fact, some of the clothing attributed to Nabi in museums do have short sleeves, even though this isn't proof.

It is for this reason, that the normally very strict author of Ahsan al-Fatawa, Mufti Rashid Ahmed Ludhyanwi, clearly gave permission for salah with a short sleeve kurta.
Se Ahsan al-Fatawa Vol. 3 Pg. 407-408.

And Allah Ta'ala knows best